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Simplifying 539x + -0.5x2 = 135600 Solving 539x + -0.5x2 = 135600 Solving for variable 'x'. Reorder the terms: -135600 + 539x + -0.5x2 = 135600 + -135600 Combine like terms: 135600 + -135600 = 0 -135600 + 539x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 271200 + -1078x + x2 = 0 Move the constant term to the right: Add '-271200' to each side of the equation. 271200 + -1078x + -271200 + x2 = 0 + -271200 Reorder the terms: 271200 + -271200 + -1078x + x2 = 0 + -271200 Combine like terms: 271200 + -271200 = 0 0 + -1078x + x2 = 0 + -271200 -1078x + x2 = 0 + -271200 Combine like terms: 0 + -271200 = -271200 -1078x + x2 = -271200 The x term is -1078x. Take half its coefficient (-539). Square it (290521) and add it to both sides. Add '290521' to each side of the equation. -1078x + 290521 + x2 = -271200 + 290521 Reorder the terms: 290521 + -1078x + x2 = -271200 + 290521 Combine like terms: -271200 + 290521 = 19321 290521 + -1078x + x2 = 19321 Factor a perfect square on the left side: (x + -539)(x + -539) = 19321 Calculate the square root of the right side: 139 Break this problem into two subproblems by setting (x + -539) equal to 139 and -139.Subproblem 1
x + -539 = 139 Simplifying x + -539 = 139 Reorder the terms: -539 + x = 139 Solving -539 + x = 139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539' to each side of the equation. -539 + 539 + x = 139 + 539 Combine like terms: -539 + 539 = 0 0 + x = 139 + 539 x = 139 + 539 Combine like terms: 139 + 539 = 678 x = 678 Simplifying x = 678Subproblem 2
x + -539 = -139 Simplifying x + -539 = -139 Reorder the terms: -539 + x = -139 Solving -539 + x = -139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539' to each side of the equation. -539 + 539 + x = -139 + 539 Combine like terms: -539 + 539 = 0 0 + x = -139 + 539 x = -139 + 539 Combine like terms: -139 + 539 = 400 x = 400 Simplifying x = 400Solution
The solution to the problem is based on the solutions from the subproblems. x = {678, 400}
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